In the oil and gas industry, seismic prospecting techniques are commonly used to aid in the search for and evaluation of subterranean hydrocarbon deposits. A seismic prospecting operation consists of three separate stages: data acquisition, data processing, and data interpretation. The success of a seismic prospecting operation is dependent on satisfactory completion of all three stages. Petroleum engineers know how to produce hydrocarbons from reserves found by a successful prospecting operation.
In the data acquisition stage, a seismic source is commonly used to generate a physical impulse known as a “seismic signal” that propagates into the earth and is at least partially reflected by subsurface seismic reflectors (i.e., interfaces between underground formations having different acoustic impedances). The reflected signals (known as “seismic reflections”) are detected and recorded by an array of seismic receivers located at or near the surface of the earth, in an overlying body of water, or at known depths in boreholes. The seismic energy recorded by each seismic receiver is known as a “seismic data trace.”
During the data processing stage, the raw seismic data traces recorded in the data acquisition stage are refined and enhanced using a variety of procedures that depend on the nature of the geologic structure being investigated and on the characteristics of the raw data traces themselves. In general, the purpose of the data processing stage is to produce an image of the subsurface geologic structure from the recorded seismic data for use during the data interpretation stage. The image is developed using theoretical and empirical models of the manner in which the seismic signals are transmitted into the earth, attenuated by the subsurface strata, and reflected from the geologic structures. The quality of the final product of the data processing stage is heavily dependent on the accuracy of the procedures used to process the data.
The purpose of the data interpretation stage is to determine information about the subsurface geology of the earth from the processed seismic data. For example, data interpretation may be used to determine the general geologic structure of a subsurface region, or to locate potential hydrocarbon reservoirs, or to guide the development of an already discovered reservoir. Obviously, the data interpretation stage cannot be successful unless the processed seismic data provide an accurate representation of the subsurface geology.
Typically, some form of seismic migration (also known as “imaging”) must be performed during the data processing stage in order to accurately position the subsurface seismic reflectors. The need for seismic migration arises because variable seismic velocities and dipping reflectors cause seismic reflections in unmigrated seismic images to appear at incorrect locations. Seismic migration is an inversion operation in which the seismic reflections are moved or “migrated” to their true subsurface positions.
There are many different seismic migration techniques. Some of these migration techniques are applied after common-midpoint (CMP) stacking of the data traces. (As is well known, CMP stacking is a data processing procedure in which a plurality of seismic data traces having the same source-receiver midpoint but different offsets are summed to form a stacked data trace that simulates a zero-offset data trace for the midpoint in question.) Such “poststack” migration can be done, for example, by integration along diffraction curves (known as “Kirchhoff” migration), by numerical finite difference or phase-shift downward-continuation of the wavefield, or by equivalent operations in frequency-wavenumber or other domains.
Conversely, other seismic migration techniques are applied before stacking of the seismic data traces. In other words, these “prestack” migration techniques are applied to the individual nonzero-offset data traces and the migrated results are then stacked to form the final image. Prestack migration typically produces better images than poststack migration. However, prestack migration is generally much more expensive than poststack migration. Accordingly, the use of prestack migration has typically been limited to situations where poststack migration does not provide an acceptable result, e.g., where the reflectors are steeply dipping.
In some cases, reflector dip can exceed 90 degrees. As is well known in the seismic prospecting art, it may be possible to image these “overturned” reflectors using data from seismic “turning rays.” Prestack migration techniques must be used in order to obtain an accurate image of overturned reflectors from seismic turning ray data.
There are two general types of prestack migration, prestack time migration and prestack depth migration. A background seismic wave propagation velocity model to describe the seismic wave propagation velocity in the subsurface is needed in the seismic imaging. In a region where the subsurface seismic wave velocity varies only in the vertical direction, the seismic imaging method used is pre-stack time migration (PSTM). In a region where the subsurface seismic wave propagation velocity varies in both vertical and lateral (or horizontal) direction, pre-stack depth migration (PSDM), needs to be used to give accurate results.
Both vertical time and lateral position errors occur in time migration whenever there are lateral velocity variations in the subsurface. See, for example, “Plumes: Response of Time Migration to Lateral Velocity Variation”, by Bevc, et al., Geophysics 60, pp. 1118-1127 (1995); or “Systematics of Time Migration Errors”, by Black and Brzostowski, Geophysics 59, pp. 1419-1434 (1994). Mild lateral velocity variations may be approximately compensated by interpolating multiple velocity functions or multiple travel time tables from different locations when the PSTM is performed in space domain, as in the Kirchhoff summation algorithm. See, for example, Seismic Data Processing, by O. Yilmaz, Society of Exploration Geophysics, pages 269-271 (1987). A common offset seismic section is defined as the seismic section of the same source-receiver spacing (offset). PSTM of a common offset section in the frequency-wavenumber (k,ω) domain is much more efficient than in real space. See, for example, “Recursive Wavenumber-Frequency Migration”, by Kim, et al., Geophysics 54, pp. 319-329 (1989); or the Finn and Winbow reference cited below. However, there is no known way to treat mild lateral velocity variations in the Fourier domain similar to the methods used in the space domain. Very often, the water bottom may have a small dip in a marine survey, or the subsurface velocity may have an increasing or decreasing trend along a specific lateral direction. These lateral velocity variations are usually big enough to cause errors, particularly in the lateral position of steeply dipping reflectors, when the traditional PSTM is applied using a single laterally-invariant velocity function. Full PSDM will properly position seismic images. However it is far more expensive than PSTM.
A current method used to compensate the errors caused by the mild lateral velocity variations is to do residual move-out correction (lining up images of different offsets by shifting the image vertically) before the final stack (adding images of different offsets together). The purpose of this residual move-out correction is to enhance the final stack image. It can not correct the lateral position error. It can not focus diffraction energy correctly. Therefore, it will loose the sharpness of fault images and give incorrect reflector dips (Bevc, 1995). The correction to the lateral velocity variations should be incorporated into the migration operator in order to correct both the vertical time error and the lateral positioning error.
What is needed is a practical method for accounting for mild lateral velocity variations in the frequency-wavenumber domain. The present invention provides such a method.